picture a square that is n times n, grid size 1. cut it diagonaly, you have n²/2, but that leaves out the bunch of triangles that are 1/2 each. how many of these triangles are there? n.
so we are left with n²/2 + n/2.
which is (n² + n)/2.
which is n(n + 1)/2.
edit.: maybe using an irl example like counting steps on a staircase and their area could help ilustrate it better, idk.
deleted by creator
picture a square that is n times n, grid size 1. cut it diagonaly, you have n²/2, but that leaves out the bunch of triangles that are 1/2 each. how many of these triangles are there? n.
so we are left with n²/2 + n/2.
which is (n² + n)/2.
which is n(n + 1)/2.
edit.: maybe using an irl example like counting steps on a staircase and their area could help ilustrate it better, idk.